158 ANNVAL REPORT SMTTHSONTAN ESrSTITDTION, 1964 



physical investigations predominate in the planetaiy research activ- 

 ities of the Observatory and much of the scientific community. 



Scientists of the Observatory, using precise satellite-tracking data 

 from the network of Baker-Nunn cameras,^ investigate three major 

 geophysical topics: the detailed representation of the earth's gravi- 

 tational field; the geometrical relation between points on the earth's 

 surface; and the density and temperature of the upper atmosphere 

 and their variations. These topics are interrelated in a way that 

 requires that they be investigated concurrently. The dire.ctor of the 

 Observatory is responsible for initiating the coordinated attack on 

 these problems and for monitormg their interaction with national and 

 international programs. 



As a satellite moves in its orbit, the details of its motion reflect 

 the many irregularities in the gravitational field corresponding to the 

 nonuniform mass distribution within the earth. The gravitational 

 potential is conventionally represented mathematically as a series ex- 

 pansion in spherical harmonics. Imre G. Izsak has used a total of 

 26,447 precisely reduced Baker-Nunn observations of 11 objects to 

 obtain least-squares estimates for the coefficients of tesseral and sec- 

 torial harmonics of the geopotential.^ The method yields estimates 

 of geophysical significance for harmonics up to the sixth degree. 

 Evaluations of zonal-harmonics coefficients in the earth's gravita- 

 tional potential up to the 14th order have been made by Dr. Y. Kozai,^ 

 who used precisely reduced Baker-Nunn observations of 1959 al, 1959 

 Eta, 1960 t2, 1961 Nu, 1961 al and 2, 1961 aSl, and 1962 ae, inclina- 

 tions of which are between 28° and 95°. 



A basic computer program used in all analyses of satellite motions 

 is the Differential Orbit Improvement program (DOT), which has 

 been extended by Mr. Izsak, M. J. Davies, and E. M. Gaposchkin 

 to incorporate the effects of the tesseral harmonics in the geopotential.^ 



Dr. Walter Kohnlein has analyzed the geometrical structure of 

 the earth's gravitational field in the harmonic representation.^ Of 

 particular interest were the shapes of the surfaces of constant po- 

 tential (geoid) and constant gra^nty, their Gaussian and mean curva- 

 tures, and the curvature and torsion of the plumb lines. 



Theoretical studies by Dr. Chi-yuen Wang on the correlation be- 

 tween the satellite-derived geoid and the heat flow distribution on 

 the surface of the earth have justified the hypothesis that the irregu- 

 lar undulations of the satellite geoid can be explained as the conse- 

 quence of uneven thermal expansion of the earth's mantle, result- 

 ing from some heating process, perhaps an inhomogeneous distribution 

 of radioactive heat sources.^ Computation of variations of temperature 

 corresponding to several proposed models of distribution of heat 



See footnotes, p. 177. 



